In an early chapter of Dracula, the Count gives a long monologue to the narrator Jonathan Harker about his family's heritage, in which he claims his Szekely heritage (even distinct from Magyar Hungarians):
“We Szekelys have a right to be proud, for in our veins flows the blood of many brave races who fought as the lion fights, for lordship. [...] And when the Hungarian flood swept eastward, the Szekelys were claimed as kindred by the victorious Magyars, and to us for centuries was trusted the guarding of the frontier of Turkey-land; ay, and more than that, endless duty of the frontier guard, for, as the Turks say, ‘water sleeps, and enemy is sleepless.’ [...] Again, when, after the battle of Mohács, we threw off the Hungarian yoke, we of the Dracula blood were amongst their leaders, for our spirit would not brook that we were not free. Ah, young sir, the Szekelys—and the Dracula as their heart’s blood, their brains, and their swords—can boast a record that mushroom growths like the Hapsburgs and the Romanoffs can never reach. The warlike days are over. Blood is too precious a thing in these days of dishonourable peace; and the glories of the great races are as a tale that is told.”
I understand that Bram Stoker's actual historical research was very spotty (like Dracula claiming descent from Attila the Hun as well), but for the purposes of this question, I distinguish between the historical ruler of Wallachia and the fictional character's biography as established by Bram Stoker in the novel.
Additional questions: how accurate was Stoker with making the distinction between Magyars and Szekelys as separate ethnicities? Have Hungarians ever tried to use the fictional Dracula to promote their claims on Transylvania after the partition of Hungary? When and how did the fictional Count's nationality become ingrained as Romanian in Anglophone popular imagination, rather than the Szekely/Hungarian heritage Stoker wrote of?
Edit: I don't know why this is tagged as "Hunting and Fishing" but it's not--unless Count Dracula's dietary habits count as hunting...
accurate was Stoker with making the distinction between Magyars and Szekelys as separate ethnicities?
This is actually quite accurate, because the origins of the Székelys is a mystery and they were always considered rather different from the Magyars. During the Middle Ages, they claimed descent from the Huns and that they had lived in central Europe prior to the arrival of the Magyars. This is no longer accepted, and three alternative theories have been put forth instead: descendants of Pannonian Avars, a Turkic people, or simply ethnic Hungarians singled out as border guards.
(like Dracula claiming descent from Attila the Hun as well)
Again, this is actually true in the sense that, from the High Middle Ages, the Székelys claimed descent from the Huns and the idea was not questioned until the late 19th century. The first Hungarian royal dynasty, the House of Árpád, also claimed descent from Attila the Hun.
As to whether or not the Árpáds' descent from Attila was actually true, the best answer anyone has been able to come with is, "Who the hell knows?" The origins of the Huns is a big question mark and so is the question of whether their language was Indo-European, Turkish, or Finno-Ugric. Tracing the descent of people during a time when literacy was extremely low is close to impossible and royalty and aristocracy claiming descent they didn't actually have was extremely common. (For instance, the Italian Colonna and Orsini families both claimed descent from the Julio-Claudian dynasty,)
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Have Hungarians ever tried to use the fictional Dracula to promote their claims on Transylvania after the partition of Hungary.
I doubt it. I haven't across anything that would indicate this to be the case and besides, Stoker's book was not well-known in central Europe until very recently. When Western tourists started traveling in droves to Romania during the 1970s looking for the "real" Dracula, most of locals had never heard of the book or its fictional Count, primarily because it was not fully and officially translated into Romanian until 1990.
Besides, using the villain of a novel to bolster your claims to territory would be rather odd, but stranger things have happened.
When and how did the fictional Count's nationality become ingrained as Romanian in Anglophone popular imagination, rather than the Szekely/Hungarian heritage Stoker wrote of?
It's because, in the original novel, Count Dracula is explicitly said to be from the country of Romania, not Hungary. Then as now, the Székelys mostly lived in what's now Romania and answered, not to the King of Hungary, but the Voivode of Wallachia.
That being said, it's worth mentioning that Bela Lugosi, the source of our current mental image of Dracula, was actually half-Hungarian and half-Serbian and from the city of Lugoj in what was then part of the Kingdom of Hungary, but is now part of Romania.
Where Stoker goofed was his depiction of the Houses of Basarab and Drăculești as Székelys (assuming that he intended his fictional count to be a descendant of Vlad Țepeș) because, historically, they were ethnic Romanians. But the assumption that Stoker borrowed anything of Vlad Țepeș for his fictional count other than his nickname is no longer certain.